String bsdfs = """

vec3 BRDF_Lambert( const in vec3 diffuseColor ) {

	return RECIPROCAL_PI * diffuseColor;

} // validated

vec3 F_Schlick( const in vec3 f0, const in float f90, const in float dotVH ) {

	// Original approximation by Christophe Schlick '94
	// float fresnel = pow( 1.0 - dotVH, 5.0 );

	// Optimized variant (presented by Epic at SIGGRAPH '13)
	// https://cdn2.unrealengine.com/Resources/files/2013SiggraphPresentationsNotes-26915738.pdf
	float fresnel = exp2( ( - 5.55473 * dotVH - 6.98316 ) * dotVH );

	return f0 * ( 1.0 - fresnel ) + ( f90 * fresnel );

} // validated

// Moving Frostbite to Physically Based Rendering 3.0 - page 12, listing 2
// https://seblagarde.files.wordpress.com/2015/07/course_notes_moving_frostbite_to_pbr_v32.pdf
float V_GGX_SmithCorrelated( const in float alpha, const in float dotNL, const in float dotNV ) {

	float a2 = pow2( alpha );

	float gv = dotNL * sqrt( a2 + ( 1.0 - a2 ) * pow2( dotNV ) );
	float gl = dotNV * sqrt( a2 + ( 1.0 - a2 ) * pow2( dotNL ) );

	return 0.5 / max( gv + gl, EPSILON );

}

// Microfacet Models for Refraction through Rough Surfaces - equation (33)
// http://graphicrants.blogspot.com/2013/08/specular-brdf-reference.html
// alpha is "roughness squared" in Disney’s reparameterization
float D_GGX( const in float alpha, const in float dotNH ) {

	float a2 = pow2( alpha );

	float denom = pow2( dotNH ) * ( a2 - 1.0 ) + 1.0; // avoid alpha = 0 with dotNH = 1

	return RECIPROCAL_PI * a2 / pow2( denom );

}

// GGX Distribution, Schlick Fresnel, GGX_SmithCorrelated Visibility
vec3 BRDF_GGX( const in vec3 lightDir, const in vec3 viewDir, const in vec3 normal, const in vec3 f0, const in float f90, const in float roughness ) {

	float alpha = pow2( roughness ); // UE4's roughness

	vec3 halfDir = normalize( lightDir + viewDir );

	float dotNL = saturate( dot( normal, lightDir ) );
	float dotNV = saturate( dot( normal, viewDir ) );
	float dotNH = saturate( dot( normal, halfDir ) );
	float dotVH = saturate( dot( viewDir, halfDir ) );

	vec3 F = F_Schlick( f0, f90, dotVH );

	float V = V_GGX_SmithCorrelated( alpha, dotNL, dotNV );

	float D = D_GGX( alpha, dotNH );

	return F * ( V * D );

}

// Rect Area Light

// Real-Time Polygonal-Light Shading with Linearly Transformed Cosines
// by Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt
// code: https://github.com/selfshadow/ltc_code/

vec2 LTC_Uv( const in vec3 N, const in vec3 V, const in float roughness ) {

	const float LUT_SIZE = 64.0;
	const float LUT_SCALE = ( LUT_SIZE - 1.0 ) / LUT_SIZE;
	const float LUT_BIAS = 0.5 / LUT_SIZE;

	float dotNV = saturate( dot( N, V ) );

	// texture parameterized by sqrt( GGX alpha ) and sqrt( 1 - cos( theta ) )
	vec2 uv = vec2( roughness, sqrt( 1.0 - dotNV ) );

	uv = uv * LUT_SCALE + LUT_BIAS;

	return uv;

}

float LTC_ClippedSphereFormFactor( const in vec3 f ) {

	// Real-Time Area Lighting: a Journey from Research to Production (p.102)
	// An approximation of the form factor of a horizon-clipped rectangle.

	float l = length( f );

	return max( ( l * l + f.z ) / ( l + 1.0 ), 0.0 );

}

vec3 LTC_EdgeVectorFormFactor( const in vec3 v1, const in vec3 v2 ) {

	float x = dot( v1, v2 );

	float y = abs( x );

	// rational polynomial approximation to theta / sin( theta ) / 2PI
	float a = 0.8543985 + ( 0.4965155 + 0.0145206 * y ) * y;
	float b = 3.4175940 + ( 4.1616724 + y ) * y;
	float v = a / b;

	float theta_sintheta = ( x > 0.0 ) ? v : 0.5 * inversesqrt( max( 1.0 - x * x, 1e-7 ) ) - v;

	return cross( v1, v2 ) * theta_sintheta;

}

vec3 LTC_Evaluate( const in vec3 N, const in vec3 V, const in vec3 P, const in mat3 mInv, const in vec3 rectCoords[ 4 ] ) {

	// bail if point is on back side of plane of light
	// assumes ccw winding order of light vertices
	vec3 v1 = rectCoords[ 1 ] - rectCoords[ 0 ];
	vec3 v2 = rectCoords[ 3 ] - rectCoords[ 0 ];
	vec3 lightNormal = cross( v1, v2 );

	if( dot( lightNormal, P - rectCoords[ 0 ] ) < 0.0 ) return vec3( 0.0 );

	// construct orthonormal basis around N
	vec3 T1, T2;
	T1 = normalize( V - N * dot( V, N ) );
	T2 = - cross( N, T1 ); // negated from paper; possibly due to a different handedness of world coordinate system

	// compute transform
	mat3 mat = mInv * transposeMat3( mat3( T1, T2, N ) );

	// transform rect
	vec3 coords[ 4 ];
	coords[ 0 ] = mat * ( rectCoords[ 0 ] - P );
	coords[ 1 ] = mat * ( rectCoords[ 1 ] - P );
	coords[ 2 ] = mat * ( rectCoords[ 2 ] - P );
	coords[ 3 ] = mat * ( rectCoords[ 3 ] - P );

	// project rect onto sphere
	coords[ 0 ] = normalize( coords[ 0 ] );
	coords[ 1 ] = normalize( coords[ 1 ] );
	coords[ 2 ] = normalize( coords[ 2 ] );
	coords[ 3 ] = normalize( coords[ 3 ] );

	// calculate vector form factor
	vec3 vectorFormFactor = vec3( 0.0 );
	vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 0 ], coords[ 1 ] );
	vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 1 ], coords[ 2 ] );
	vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 2 ], coords[ 3 ] );
	vectorFormFactor += LTC_EdgeVectorFormFactor( coords[ 3 ], coords[ 0 ] );

	// adjust for horizon clipping
	float result = LTC_ClippedSphereFormFactor( vectorFormFactor );

/*
	// alternate method of adjusting for horizon clipping (see referece)
	// refactoring required
	float len = length( vectorFormFactor );
	float z = vectorFormFactor.z / len;

	const float LUT_SIZE = 64.0;
	const float LUT_SCALE = ( LUT_SIZE - 1.0 ) / LUT_SIZE;
	const float LUT_BIAS = 0.5 / LUT_SIZE;

	// tabulated horizon-clipped sphere, apparently...
	vec2 uv = vec2( z * 0.5 + 0.5, len );
	uv = uv * LUT_SCALE + LUT_BIAS;

	float scale = texture2D( ltc_2, uv ).w;

	float result = len * scale;
*/

	return vec3( result );

}

// End Rect Area Light


float G_BlinnPhong_Implicit( /* const in float dotNL, const in float dotNV */ ) {

	// geometry term is (n dot l)(n dot v) / 4(n dot l)(n dot v)
	return 0.25;

}

float D_BlinnPhong( const in float shininess, const in float dotNH ) {

	return RECIPROCAL_PI * ( shininess * 0.5 + 1.0 ) * pow( dotNH, shininess );

}

vec3 BRDF_BlinnPhong( const in vec3 lightDir, const in vec3 viewDir, const in vec3 normal, const in vec3 specularColor, const in float shininess ) {

	vec3 halfDir = normalize( lightDir + viewDir );

	float dotNH = saturate( dot( normal, halfDir ) );
	float dotVH = saturate( dot( viewDir, halfDir ) );

	vec3 F = F_Schlick( specularColor, 1.0, dotVH );

	float G = G_BlinnPhong_Implicit( /* dotNL, dotNV */ );

	float D = D_BlinnPhong( shininess, dotNH );

	return F * ( G * D );

} // validated

#if defined( USE_SHEEN )

// https://github.com/google/filament/blob/master/shaders/src/brdf.fs
float D_Charlie( float roughness, float dotNH ) {

	float alpha = pow2( roughness );

	// Estevez and Kulla 2017, "Production Friendly Microfacet Sheen BRDF"
	float invAlpha = 1.0 / alpha;
	float cos2h = dotNH * dotNH;
	float sin2h = max( 1.0 - cos2h, 0.0078125 ); // 2^(-14/2), so sin2h^2 > 0 in fp16

	return ( 2.0 + invAlpha ) * pow( sin2h, invAlpha * 0.5 ) / ( 2.0 * PI );

}

// https://github.com/google/filament/blob/master/shaders/src/brdf.fs
float V_Neubelt( float dotNV, float dotNL ) {

	// Neubelt and Pettineo 2013, "Crafting a Next-gen Material Pipeline for The Order: 1886"
	return saturate( 1.0 / ( 4.0 * ( dotNL + dotNV - dotNL * dotNV ) ) );

}

vec3 BRDF_Sheen( const in vec3 lightDir, const in vec3 viewDir, const in vec3 normal, vec3 sheenColor, const in float sheenRoughness ) {

	vec3 halfDir = normalize( lightDir + viewDir );

	float dotNL = saturate( dot( normal, lightDir ) );
	float dotNV = saturate( dot( normal, viewDir ) );
	float dotNH = saturate( dot( normal, halfDir ) );

	float D = D_Charlie( sheenRoughness, dotNH );
	float V = V_Neubelt( dotNV, dotNL );

	return sheenColor * ( D * V );

}

#endif
""";
